Frequency and Period of SHM - AP Physics 1
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What happens to the angular frequency if the period doubles?
What happens to the angular frequency if the period doubles?
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Halves. Angular frequency is inversely proportional to period.
Halves. Angular frequency is inversely proportional to period.
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What is the dimension of period?
What is the dimension of period?
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T. Period has units of time duration.
T. Period has units of time duration.
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What is the period of a pendulum with length $1 \text{ m}$ on Earth?
What is the period of a pendulum with length $1 \text{ m}$ on Earth?
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$T = 2\pi \sqrt{\frac{1}{9.8}} \approx 2.01 \text{ s}$. Using the pendulum formula with $L = 1$ m and $g = 9.8$ m/s².
$T = 2\pi \sqrt{\frac{1}{9.8}} \approx 2.01 \text{ s}$. Using the pendulum formula with $L = 1$ m and $g = 9.8$ m/s².
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If a pendulum's length is quadrupled, how does its period change?
If a pendulum's length is quadrupled, how does its period change?
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Doubles. Period scales with square root of length, so $\sqrt{4} = 2$.
Doubles. Period scales with square root of length, so $\sqrt{4} = 2$.
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What is the dimension of frequency?
What is the dimension of frequency?
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T⁻¹. Frequency has units of inverse time.
T⁻¹. Frequency has units of inverse time.
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For a mass-spring system, what is the effect of increasing mass on the period?
For a mass-spring system, what is the effect of increasing mass on the period?
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Increases the period. Period is proportional to square root of mass.
Increases the period. Period is proportional to square root of mass.
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State the formula for frequency in terms of angular frequency.
State the formula for frequency in terms of angular frequency.
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$f = \frac{\omega}{2\pi}$. Derived from $\omega = 2\pi f$, solving for frequency.
$f = \frac{\omega}{2\pi}$. Derived from $\omega = 2\pi f$, solving for frequency.
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If a mass-spring system oscillates at $10 \text{ Hz}$, what is its period?
If a mass-spring system oscillates at $10 \text{ Hz}$, what is its period?
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$T = 0.1 \text{ s}$. Using $T = \frac{1}{f} = \frac{1}{10} = 0.1$ s.
$T = 0.1 \text{ s}$. Using $T = \frac{1}{f} = \frac{1}{10} = 0.1$ s.
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How does the period of SHM change if the amplitude is doubled?
How does the period of SHM change if the amplitude is doubled?
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No change. Period is independent of amplitude in SHM.
No change. Period is independent of amplitude in SHM.
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What is the angular frequency of a system with $T = 2 \text{ s}$?
What is the angular frequency of a system with $T = 2 \text{ s}$?
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$\omega = \pi \text{ rad/s}$. Using $\omega = \frac{2\pi}{T} = \frac{2\pi}{2} = \pi$ rad/s.
$\omega = \pi \text{ rad/s}$. Using $\omega = \frac{2\pi}{T} = \frac{2\pi}{2} = \pi$ rad/s.
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Calculate the period for a simple pendulum on the Moon with $L = 1 \text{ m}$ and $g = 1.6 \text{ m/s}^2$.
Calculate the period for a simple pendulum on the Moon with $L = 1 \text{ m}$ and $g = 1.6 \text{ m/s}^2$.
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$T = 2\pi \sqrt{\frac{1}{1.6}} \approx 4.97 \text{ s}$. Using the pendulum formula with Moon's gravity.
$T = 2\pi \sqrt{\frac{1}{1.6}} \approx 4.97 \text{ s}$. Using the pendulum formula with Moon's gravity.
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What determines the period of a simple harmonic oscillator?
What determines the period of a simple harmonic oscillator?
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Mass and spring constant. These are the only factors in the period formula for springs.
Mass and spring constant. These are the only factors in the period formula for springs.
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State the effect of increasing gravity on the period of a pendulum.
State the effect of increasing gravity on the period of a pendulum.
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Decreases the period. Period is inversely proportional to square root of gravity.
Decreases the period. Period is inversely proportional to square root of gravity.
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For a spring-mass system, if $m = 9 \text{ kg}$ and $k = 36 \text{ N/m}$, find $T$.
For a spring-mass system, if $m = 9 \text{ kg}$ and $k = 36 \text{ N/m}$, find $T$.
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$T = 2\pi \sqrt{\frac{9}{36}} \approx 3.14 \text{ s}$. Using the spring-mass formula with given values.
$T = 2\pi \sqrt{\frac{9}{36}} \approx 3.14 \text{ s}$. Using the spring-mass formula with given values.
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What is the period of a wave with a frequency of $20 \text{ Hz}$?
What is the period of a wave with a frequency of $20 \text{ Hz}$?
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$T = 0.05 \text{ s}$. Using $T = \frac{1}{f} = \frac{1}{20} = 0.05$ s.
$T = 0.05 \text{ s}$. Using $T = \frac{1}{f} = \frac{1}{20} = 0.05$ s.
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What is the equation for the position of a mass in SHM as a function of time?
What is the equation for the position of a mass in SHM as a function of time?
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$x(t) = A \cos(\omega t + \phi)$. General form for position in simple harmonic motion.
$x(t) = A \cos(\omega t + \phi)$. General form for position in simple harmonic motion.
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What is the period of oscillation for a spring with $k = 100 \text{ N/m}$ and $m = 4 \text{ kg}$?
What is the period of oscillation for a spring with $k = 100 \text{ N/m}$ and $m = 4 \text{ kg}$?
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$T = 2\pi \sqrt{\frac{4}{100}} \approx 1.26 \text{ s}$. Using the spring-mass formula with given values.
$T = 2\pi \sqrt{\frac{4}{100}} \approx 1.26 \text{ s}$. Using the spring-mass formula with given values.
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Calculate the period for a spring system with $k = 200 \text{ N/m}$ and $m = 0.5 \text{ kg}$.
Calculate the period for a spring system with $k = 200 \text{ N/m}$ and $m = 0.5 \text{ kg}$.
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$T = 2\pi \sqrt{\frac{0.5}{200}} \approx 0.31 \text{ s}$. Using the spring-mass formula with given values.
$T = 2\pi \sqrt{\frac{0.5}{200}} \approx 0.31 \text{ s}$. Using the spring-mass formula with given values.
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What is the frequency of SHM when the system completes $50$ cycles in $10 \text{ s}$?
What is the frequency of SHM when the system completes $50$ cycles in $10 \text{ s}$?
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$f = 5 \text{ Hz}$. Using $f = \frac{\text{cycles}}{\text{time}} = \frac{50}{10} = 5$ Hz.
$f = 5 \text{ Hz}$. Using $f = \frac{\text{cycles}}{\text{time}} = \frac{50}{10} = 5$ Hz.
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What is the formula for angular frequency?
What is the formula for angular frequency?
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$\omega = 2\pi f = \frac{2\pi}{T}$. Angular frequency relates to linear frequency and period.
$\omega = 2\pi f = \frac{2\pi}{T}$. Angular frequency relates to linear frequency and period.
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Identify the unit of period in the International System of Units.
Identify the unit of period in the International System of Units.
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Seconds (s). Standard SI unit for time duration of one complete cycle.
Seconds (s). Standard SI unit for time duration of one complete cycle.
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Find the frequency if the angular frequency is $6\pi \text{ rad/s}$.
Find the frequency if the angular frequency is $6\pi \text{ rad/s}$.
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$f = 3 \text{ Hz}$. Using $f = \frac{\omega}{2\pi} = \frac{6\pi}{2\pi} = 3$ Hz.
$f = 3 \text{ Hz}$. Using $f = \frac{\omega}{2\pi} = \frac{6\pi}{2\pi} = 3$ Hz.
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Calculate the angular frequency for a system with frequency $8 \text{ Hz}$.
Calculate the angular frequency for a system with frequency $8 \text{ Hz}$.
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$\omega = 16\pi \text{ rad/s}$. Using $\omega = 2\pi f = 2\pi(8) = 16\pi$ rad/s.
$\omega = 16\pi \text{ rad/s}$. Using $\omega = 2\pi f = 2\pi(8) = 16\pi$ rad/s.
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What is the frequency of a simple pendulum with period $5 \text{ s}$?
What is the frequency of a simple pendulum with period $5 \text{ s}$?
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$f = 0.2 \text{ Hz}$. Using $f = \frac{1}{T} = \frac{1}{5} = 0.2$ Hz.
$f = 0.2 \text{ Hz}$. Using $f = \frac{1}{T} = \frac{1}{5} = 0.2$ Hz.
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Find the frequency if the period is $0.5 \text{ s}$.
Find the frequency if the period is $0.5 \text{ s}$.
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$f = 2 \text{ Hz}$. Using $f = \frac{1}{T} = \frac{1}{0.5} = 2$ Hz.
$f = 2 \text{ Hz}$. Using $f = \frac{1}{T} = \frac{1}{0.5} = 2$ Hz.
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What is the relationship between period and length for a pendulum?
What is the relationship between period and length for a pendulum?
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Directly proportional to $\sqrt{L}$. Period increases with square root of length.
Directly proportional to $\sqrt{L}$. Period increases with square root of length.
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Which factors affect the period of a simple pendulum?
Which factors affect the period of a simple pendulum?
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Length and gravity. These are the only factors in the period formula for pendulums.
Length and gravity. These are the only factors in the period formula for pendulums.
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What is the formula for the period of a mass-spring system?
What is the formula for the period of a mass-spring system?
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$T = 2\pi \sqrt{\frac{m}{k}}$. Period depends on mass and spring constant for elastic oscillations.
$T = 2\pi \sqrt{\frac{m}{k}}$. Period depends on mass and spring constant for elastic oscillations.
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Identify the unit of frequency in the International System of Units.
Identify the unit of frequency in the International System of Units.
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Hertz (Hz). Standard SI unit for cycles per second.
Hertz (Hz). Standard SI unit for cycles per second.
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What is the period of a pendulum with $L = 2 \text{ m}$ on Mars where $g = 3.7 \text{ m/s}^2$?
What is the period of a pendulum with $L = 2 \text{ m}$ on Mars where $g = 3.7 \text{ m/s}^2$?
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$T = 2\pi \sqrt{\frac{2}{3.7}} \approx 4.6 \text{ s}$. Using the pendulum formula with Mars gravity.
$T = 2\pi \sqrt{\frac{2}{3.7}} \approx 4.6 \text{ s}$. Using the pendulum formula with Mars gravity.
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